Short title
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
Full Title
QM11
Henrik Qvigstad
henrik.qvigstad@fys.uio.no
University of Oslo
June 17, 2011
Short title
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
1 Photons as a signature of QGP
Photons through annihilation
Photonst through the Compton Process
Photon production by quark annihilation in QGP
Photon Production in Heavy Ion Collisions
2 Quark Matter 2011
Short title
H. Qvigstad
Photons as a signature of QGP
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
Photons in the plasma can be produced through annihilation,
qq̄ → γg ,
(1)
qq̄ → γγ,
(2)
alternatively through “Compton Scattering”,
gq → γq,
(3)
g q̄ → γq̄.
(4)
(Feynman Diagrams here)
Short title
H. Qvigstad
Photons through annihilation
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
The gluon vertex is assosiated with
a
µ λij
g γαβ
2
(5)
The photon vertex(es) are associated with
µ
− ieq γαβ
(6)
Thus, the cross sections are related as
a 2
λij αs e 2
dσ
dσ
Eγ
Eγ
(qq̄ → γg ) = (qq̄ → γγ) (7)
d~pγ
2 αe eq
d~pγ
Short title
H. Qvigstad
Photons through annihilation
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
The cross-section can be written in terms of
t = (p1 − p3 )2 = (pq − pγ )2 , and it can be shown that
q
s − 4mq2 dσ p · (p + p ) √s dσ
γ
q
q̄
√
=
δ
.
−
Eγ
d~pγ
2π
dt
2
s
(8)
Futhermore, qq̄ → γγ is related to e + e − → γγ such that
e 4 dσ
dσ
q
(qq̄ → γγ) =
(e + e − → γγ)
dt
e
dt
(9)
, a cross section that is worked out in Berestetskii, et. al. 1982,
according to Wong.
Short title
Photons through annihilation
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
t − m2 = −2pg · pq = −2Eg (Eq − |~pq | cos θgq ).
(10)
The differential cross section contains terms which vary as
(t − m2 )−1 and (u − m2 )−1 . Thus the cross section is at
maximum when the produced particle momenta is parralell with
the momenta with the initial particles, i.e.
θgq , θγq̄ {0, π}.
(11)
Furthermore, expanding the (t − m2 )−1 around θgq show that
the the width of the peak, ∆θgq , is
m
.
(12)
∆θgq =
Eq̄
Thus, for the relativistic case,
Eγ
dσ
1
(qq̄ → γγ) = σqq̄→γγ (s) Eg [δ(~pγ − ~pq ) + δ(~pγ − ~pq̄ )].
d~pγ
2
(13)
Short title
Photons through annihilation
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
The total cross section for e + e − → γγ is also worked out in
Berestetskii, and by using the previous
QM11
σqq̄→γg (s) =
e 2 4πα α
q
e s
(14)
e( s − 4m2
!
√
√
4m2 16m4
s + s − 4m2
√
×
1+
− 2
ln √
s
s
s − s − 4m2
)
r
4m2
4m2
− 1+
1−
.
s
s
Thus, for the relativistic case
a 2 o
λij eq 2 4παe αs n s σqq̄→γg (s) = ln
−
1
2
e
s
m2
(15)
Short title
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
Photons through the Compton
Process
Another source of photons in the plasma are through
QM11
gq → γq,
(16)
g q̄ → γq̄.
(17)
This process is analogous to the Compton Reaction, where a
photon scatters of a charged particle, and are therefrore called
the Compton Process.
As for the case of qq̄ annihilation, we may write
a 2
λij αs e 2
dσ
dσ
Eγ
(g q̄ → γg ) = (γq → γq) (18)
Eγ
d~pγ
2 αe eq
d~pγ
Short title
Photons through the Compton
Process
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
Also, as for qq̄,the cross section contains (t − m2 )−1 and
(u − m2 )−1 terms. So, maximum and width is again at
θgq , θγq̄ {0, π}.
∆θgq =
m
,
Eq̄
(19)
(20)
and for the relativistic case
Eγ
dσ
1
(gq → γq) = σqq̄→γγ (s) Eγ δ(~pγ − ~pq ).
d~pγ
2
a 2 λij eq 2 4παe αs
s
1
σqq̄→γg (s) = ln
+
2
e
s
m2
2
(21)
(22)
Short title
Photon Production in the plasma
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
Using the approximation of ~pγ = ~pq , photon production due to
annihilation (qq̄ → γg ) in the plasma is given by
Eγ
dNγann
4Ns2
=
fq (~pγ )
(23)
d~pγ d 4 x
(2π)6
p
XZ
s(s − 4m2 )
3
×
.
d pq̄ fq̄ (~pq̄ )[1 + fg (~pq̄ )]σ̄qf q̄f →γg (s)
2Eq̄
f
Similarly, production due to Compton Process ((gq → γq)) is
given by
Eγ
dNγcom (gq → γq)
4Ns N
=
fq (~pγ )
(24)
4
d~pγ d x
(2π)6
XZ
s − m2
×
d 3 pg fg (~pg )[1 − fg (~pg )]σ̄gqf →γqf (s)
2Eg
f
Short title
H. Qvigstad
Photon Production in the plasma
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
Using Fermi-Dirac for fq , Bose-Einstein for fg , the relativistic
approximation, and u & d quarks,
for annihilation
dNγann
4Eγ T
5 αe αs
2
=
Eγ
fq (~pγ )T ln
+ Cann
(25)
d~pγ d 4 x
9 (2π)2
m2
The result for compton scattering is similar, such that the total
for the two is
dNγann
4Eγ T
5 αe αs
2
=
fq (~pγ )T 2ln
+ Cann + Ccomp
Eγ
d~pγ d 4 x
9 (2π)2
m2
(26)
Short title
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
Photon Production by Hadrons
In addition annihilation and compton scattering of quarks,
interaction hadrons in the plasma leads to photon production;
i.g. the annihilation
π + + π − → γ + ρ0 ,
±
0
±
π +π →γ+π ,
(27)
(28)
and compton scattering;
π ± + ρ0 → γ + π ± ,
±
∓
(29)
0
π +ρ →γ+π ,
(30)
π 0 + ρ± → γ + π ±
(31)
The processes are analogous to the ones previously discussed.
Short title
Key Lesson
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
The Key Lessons is:
• The spectrum of photons production in the Thermal
Medium is virtually same (proportional) as/to the
spectrum of momentum for its origin (quark/hadron).
• For a thermal QGP, Fermi-Dirac and Bose-Einstein, the
high energy spectrum is
dNγ
∝ e −Eγ /T
dEγ
(32)
Short title
Collision Evolution
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
(Light cone image)
Short title
Collision Evolution
H. Qvigstad
Expansion and temperature
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
• As the system expands, energy density, pressure, and
Temperature decreases,
• thus we are are probing not one temperature, but the
photons from a continuum of temperatures.
(nice image from QM showing calculation of shift of spectrum)
Short title
H. Qvigstad
Photons in
QGP
Collision Evolution
Background
Annahilation
Compton
Plasma
HIC
QM11
Photons are also produced in the other stages of a HIC,
• the pre-QGP phase:
• Direct Photons, i.e. binary collisions,
• and production in pre-equilibrated Collision Matter,
• and the post-QGP phase:
• Latency heat????
• production in the Hadron Gas,
• and as decay products of final state produced particles.
Short title
H. Qvigstad
Critical d+Au Check
Photons in
QGP
Annahilation
Compton
Plasma
HIC
8
QM11

New:
 no exponential excessin
d+Au
Poster: Y. Yamaguchi
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
Short title
H. Qvigstad
Confirmation fromd+Au and Cu+Cu
Photons in
QGP
Annahilation
Compton
Plasma
HIC
51

Fraction of direct photonscompared to pQCD
QM11
Noexcessind+Au
(nomedium)
ExcessalsoinCu+Cu
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
Short title
H. Qvigstad
Direct Photon v2
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
11
preliminary
Au+Au@200GeV
minimumbias

p0 v2

p0 v2 similar to inclusive
photon v2
Two possibilities
 A:
there are no direct
photons
 B: direct photon v2 similar
to inclusive photon v2
inclusivephoton v2

Key: precisemeasurement
of direct photon excess
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
Short title
H. Qvigstad
Direct Photon v2
Photons in
QGP
Annahilation
Compton
Plasma
HIC
QM11
12
Au+Au@200GeV
minimumbias
direct photon v2 large
(~15%) at pT =2.5GeV
 v2  0where prompt
photonsdominate

Direct photon v2
preliminary
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
Short title
H. Qvigstad
TheoryComparison: Direct Photon v2
Photons in
QGP
Annahilation
Compton
Plasma
HIC
13
Theorycalculation:
Holopainen, Räsänen, Eskola
arXiv:1104.5371v1
QM11
preliminary



Modelsunder-predict
direct photon v2
Measurement further
constrains Ti andt i
Challengeto theorists
Plenary: S. Esumi (flow),Tue
Parallel: E. Kistenev(directphotons)Thu
Stefan Bathe for PHENIX, QM2011
Figure: From PHENIX flow talk by S. Esumi, QM11
Short title
H. Qvigstad
Photons in
QGP
Annahilation
Compton
Plasma
HIC
All togethernow
SummaryofRAA resultsinvariouschannels,withreferences
QM11
17
Figure: From PHENIX RAA talk by Martin L. Purschke, , QM11
Isolated photon R AA vs NPart
Short title
H. Qvigstad
Photons in
QGP
30-100%
MB 10-30%
Annahilation
Compton
Plasma
HIC
0-10%
QM11
20-25 GeV
30-40 GeV
25-30 GeV
40-50 GeV
50-80 GeV
No centrality dependence
Yen-J ie Lee(MIT)
Nuclear Modification factors from the CMS experiment
Quark Matter 2011
19
Figure: From CMS Nuclear Modification Factor talk by Yen J Lee,
QM11
Short title
H. Qvigstad
Isolated photon R AA in 0-10% PbPb collisions
PbPb 0-10% Photon R AA
Photons in
QGP
Annahilation
Compton
Plasma
HIC
PbPb(EPS09,nDS,HKN07)/pp(CT10)
Pb+Pb
QM11
E TIso <5 GeV


CMS measured the isolated photon R AA for the first time
The photon R AA at 0-10% is consistent with unity
Yen-J ie Lee(MIT)
Nuclear Modification factors from the CMS experiment
Quark Matter 2011
18
Figure: From CMS Nuclear Modification Factor talk by Yen J Lee,
QM11